Application of Generalized Probability Weighted Moments for Skew Normal Distribution

Authors

  • E. A. Elsherpieny Institute of Statistical Studies and Research, Cairo University, Cairo
  • Amal S. Hassan Institute of Statistical Studies and Research, Cairo University, Cairo
  • Neema M. El Haroun Institute of Statistical Studies and Research, Cairo University, Cairo

Keywords:

Probability weighted Moments, Generalized probability weighted Moments, Fractional moments and Skew normal distribution

Abstract

Skewness is often present in a wide range of applied problems. One possible approach to model this skewness is based on the class of skew normal distributions. This article focuses on estimating the unknown parameters of skew normal distribution. Generalized probability weighted moments, probability weighted moments and fractional moments estimating methods are investigated in skew normal distribution. Comparison between estimators is made through Monte Carlo simulation via their mean square errors. Comparison study revealed that the fractional moment estimators are better than generalized probability weighted moment and probability weighted moment estimators

 

 

References

Abdul Khalique." Estimation by Fractional moments". Developments in Statistics and Its Applications, 553-562, 1983.

Ashkar, F. and Mahdi ,S. “Comparison of two fitting methods for the log logistic distribution “. Water Resources Research, 39, 1-7, 2003.

Azzalini, A." A class of distributions which includes the normal ones, Scandinavian" Journal of Statistics, 12, 171-178, 1985.

Bayes, c., and Branco, M. " Bayesian inference for the skewness parameter of scalar skew normal Distribution" Brazilian Journal of Probability and Statistics. 21, 141-163, 2007.

Elharoun, N.M.“Generalized Probability Weighted Moments Estimators for Some Distributions“.. M.Sc. Thesis, Cairo University 2009.

Flecher, C. Naveau, P. and Allard, D. "Estimating the Closed Skew-Normal parameters using weighted moments". Statistics & Probability Letters, 79, 1977-1984, 2009.

Greenwood, J.A., Landweher, J.M., Matalas, N.C., and Wallis, J.R. "Probability Weighted Moments: definition and Relation to Parameters of Several Distributions Expressible in Inverse Form". Water Resources Research, 15, .5, 1049-1054, 1979.

Gupta, R. C. and Brown, N. "Reliability studies of the skew-normal distribution and its application to a strength-stress model, Communications in Statistics" Theory and Methods, 30, 2427-2445, 2001.

Henze, N. A probabilistic representation of the skew-normal distribution, Scandinavian Journal of Statistics, 13, 271-275, 1986.

Hosking, J. R. M. "The Theory of Probability Weighted Moments". Research Report RC 12210, IBM Research Division, Yorktown Heights, NY, 1986.

Landweher, J.M., Matalas, N.C., and Wallis, J.R. "Probability Weighted Moments Compared with some Traditional Techniques in Estimating Gumbel Parameters and Quantiles". Water Resources Research, 15, 1055-1064, 1979.

Mahdi, S. and Ashkar, F. “ Exploring Generalized Probability Weighted Moments, Generalized Moments and Maximum Likelihood Estimating Methods in Two-Parameter Weibull Model“. Journal. of Hydrology, 285, 62-77, 2004.

Pewsey, A. "The wrapped skew-normal distribution on the circle, Communications in Statistics" Theory and Methods, 29, 2459-2472, 2000.

Rasmussen, P. "Generalized Probability Weighted Moment: Application to the Generalized Pareto Distribution". Water Resources Research, 37, 6, 1745-1751, 2001.

Song, D., and Ding, J. "The application of probability weighted moments in estimating the parameters of the Pearson type three distributions". Journal of Hydrology, 101,47-61, 1988.

Downloads

Published

2014-02-14

How to Cite

Elsherpieny, E. A., Hassan, A. S., & El Haroun, N. M. (2014). Application of Generalized Probability Weighted Moments for Skew Normal Distribution. Asian Journal of Applied Sciences, 2(1). Retrieved from https://www.ajouronline.com/index.php/AJAS/article/view/650

Issue

Vol. 2 No. 1 (2014): February 2014

Section

Articles

License

  • Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
  • It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
  • The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
  • The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
  • The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.